How the flash mind reader works:

If you take any two-digit number, add the digits together, then subtract the sum from the original number, the result is always a multiple of nine. Yes, it really is. Keep that in mind. The table of numbers and hieroglyphs to the right of the 'crystal ball' changes every time you play (it's not static as I thought at first), and every time it changes, all multiples of nine have the same symbol. It doesn't matter what number you start with, the result is going to be a multiple of nine and therefore the corresponding hieroglyph will be displayed! ..so that's how this is done. Clever.